Jean-Michel Muller, the father of the French computer arithmetic community

Jean-Michel Muller is undoubtedly a pioneer in digital computing! As Director of Research at the CNRS at the LIP (Laboratory of Parallel Computing) laboratory, he was one of the first to work on computer arithmetic in France. It is thanks to him that French expertise has developed so much and is so well recognised internationally.

‘I think that if I am sometimes referred to as the father of this community,’ he confides, ‘it is mainly because I am at the head of a veritable scientific lineage. Those in France who work on the subject and have contributed to its growth are almost all former doctoral students, and their own students...’

A passion for research, combining mathematics and computer science

What drives him? ‘It's knowledge, the desire to learn and understand!’ After graduating from Ensimag in 1983, Jean-Michel Muller quickly realised that he was cut out for research and sought out the professors who inspired him most, particularly François Robert, a pioneer in neural networks in Grenoble, among other things. ‘I did my thesis in applied mathematics in his team at the Institut National Polytechnique de Grenoble, under the supervision of Michel Cosnard, who later became president of Inria.’

Michel Cosnard then joined the ENS in Lyon, and Jean-Michel Muller followed him in 1989, with an exciting prospect: to participate in the creation of the ENS's computer science laboratory. Here, the CNRS welcomed him as a research fellow. He took the opportunity to set up a computer arithmetic team in Lyon.

In concrete terms, what does computer arithmetic consist of? It encompasses all the methods, circuits and algorithms that enable calculations to be performed on machines, with reliability being the primary concern. ‘All calculations are built on top of the arithmetic of our machines. If we compromise on reliability, it's like building on quicksand,’ explains Jean-Michel Muller. The difficulty is that computers can only represent a limited number of values. And with each calculation, a small rounding error can creep in. Multiplied by billions of operations, micro-errors can accumulate and skew the results.'

The solution favoured by the researcher and his team was to ensure that each operation and each function produced a result as close as possible to the exact theoretical result. Subsequently recommended through an international standard, this property, known as ‘correct rounding’, enables the design of more accurate algorithms and, ultimately, more efficient software and computer circuits. In this context, Jean-Michel Muller and his colleagues also helped solve a thorny arithmetic problem known as the ‘table maker's dilemma’. The solution consists of determining, among the numbers that can be represented by a machine, which one has a mathematical function (such as exponentials and sines) closest to the midpoint between two consecutive numbers.

Today, the team to which Jean-Michel Muller has contributed for over 30 years, shared between Inria, the CNRS, the ENS Lyon and Claude Bernard Lyon 1 University, has become a global benchmark. First named Arénaire, in reference to Archimedes' treatise on large numbers, then AriC, it is now called Pascaline, after the calculating machine invented by Blaise Pascal. His work has flourished through large-scale international collaborations, notably with Milos Ercegovac from the United States and Peter Kornerup from Denmark. Together with them, Jean-Michel Muller has organised leading conferences in the field, such as ARITH (International Symposium on Computer Arithmetic).

'Our work was based on interactions with scientists from various disciplines: experts in number theory, circuits, source code translation programmes into machine language, computer-assisted proof... This interdisciplinary approach is particularly enriching!' Jean-Michel Muller now focuses on passing on his knowledge to young researchers and through the books he has written, which are regularly reprinted. A valuable scientific legacy.